Thermodynamics: SFEE Homework Solution

[JamesB93]

Homework Statement

This is a question from an exam that my university determined to be so harsh that they allowed resits with uncapped grades. I'm going to be taking such a resit thus I'm trying to figure out the paper:

Air at 10^oC and 80 kPa enters the diffuser of a jet engine steadily with a velocity of 200m/s and a specific enthalpy of 283.14kJ/kg. The inlet area of the diffuser is 0.4m². The air leaves the diffuser with a velocity that is very small compared with the inlet velocity.

Determine:

a) The mass flow rate of the air (5 marks)

b) The enthalpy of the air leaving the diffuser (5 marks)

Homework Equations

pv=mRT
modified SFEE: h₁ + c₁²/2 = h₂ + c₂²/2

volumetric flow = velocity x inlet area

R = 287J/kg/K

The Attempt at a Solution

[/B]
a) VF = 200m/s * 0.4m² = 80m³/s
mass flow = (pressure x volumetric flow rate)/(gas constant of air x temperature)
mass flow = (80000 x 80)/(287 x 283.15) = 78.76kg/s

b) for this section I have no idea, all I can say is that the enthalpy is very large in comparison with the inlet. I have been given no values as far as I can tell.

 

[JamesB93]

Homework Statement

This is a question from an exam that my university determined to be so harsh that they allowed resits with uncapped grades. I'm going to be taking such a resit thus I'm trying to figure out the paper:

Air at 10^oC and 80 kPa enters the diffuser of a jet engine steadily with a velocity of 200m/s and a specific enthalpy of 283.14kJ/kg. The inlet area of the diffuser is 0.4m². The air leaves the diffuser with a velocity that is very small compared with the inlet velocity.

Determine:

a) The mass flow rate of the air (5 marks)

b) The enthalpy of the air leaving the diffuser (5 marks)

Homework Equations

pv=mRT
modified SFEE: h₁ + c₁²/2 = h₂ + c₂²/2

volumetric flow = velocity x inlet area

R = 287J/kg/K

The Attempt at a Solution

[/B]
a) VF = 200m/s * 0.4m² = 80m³/s
mass flow = (pressure x volumetric flow rate)/(gas constant of air x temperature)
mass flow = (80000 x 80)/(287 x 283.15) = 78.76kg/s

b) for this section I have no idea, all I can say is that the enthalpy is very large in comparison with the inlet. I have been given no values as far as I can tell.

EDIT:

I had an idea I could just assume the exit velocity roughly to see how much difference it made. As the general guidance from the question is to give answers in kJ/kg and rounded to 2dp, a velocity of less than 3m/s makes absolutely no difference to the outcome. With the emphasis on "very small" in the question, would it be safe to assume that it's less than 3m/s (1.5% of the original)?

eg. @ 3m/s

h₁ + c₁²/2 - c₂²/2 =

283140 + (200² - 3²)/2 = h₂
283140 + 19995.5 = 303135.5J/kg = 303.14kJ/kg

 

[Chestermiller]

Why didn't you just take the exit velocity as zero?

 

[JamesB93]

Why didn't you just take the exit velocity as zero?

I was thinking that, wasn't sure if it was acceptable to do so. My lecturers haven't been too clear through this year. It gives the same result so I'm guessing that's what I'm supposed to do.

Thanks :)